It is a long-standing product requirement of rotating ball writing instruments such as the common ball-point pen that such instruments be capable of withstanding the effects of being dropped upon a hard surface such as a concrete or tile floor without damage to the instrument which would impair its writing quality. Where such writing instruments employ viscous inks or a wick or fiber-filled ink reservoir to contain less viscous inks, the problem has been relatively easy to overcome. Where, however, it is desired to use a writing instrument employing an ink of lesser viscosity such as water-based ink in a reservoir not employing a wick or fibrous absorbing member, accidental droppage can often render the writing instrument non-functional because the rotating ball will become dislodged from its socket even though the point and ball are not directly contacted by the hard surface. This is especially a problem when plastic points are used since such points usually have a ball retention force not exceeding about 0.3 pounds as compared to metal points which usually have a retention force ranging from 0.7 to 3.8 pounds. No satisfactory explanation has existed of the system kenetics leading to such ball loss.
We have made many attempts including design changes of the ball seat configuration, internal restricting of the barrel and modification of ink and grease plug follower properties to prevent such ball loss when using plastic points or other points having a low-ball retention force. While some degree of success has been achieved, none has made possible the passing of a test in which such a writing instrument is dropped upon a hard surface from a distance of three feet, simulating accidental dropping by the user.
We have analogized the phenomenon causing ball loss to that of water hammer in household pipes. This occurs when a valve is suddenly closed causing the water in the pipe to stop flowing with an abrupt increase in pressure. In order that the flowing water be brought to rest, it is necessary for the kinetic energy of the water to be transformed into potential energy and stored in available energy sinks. Energy can be stored by a compression of the water and by an expansion of the pipe walls, both due to an increase in water pressure.
The physics of a writing instrument impacting on a solid surface can be considered analogous to that of water hammer with the only difference being that the pen barrel, i.e. the pipe, is moving with the ink, i.e. the water.
Specifically, for the pen-ink system, as the ball is stopped during impact, the following series of events occur:
The first ink layer behind the ball becomes compressed due to its kinetic energy and comes to rest at an above-normal pressure. This increase in ink pressure causes the pen wall just behind the ball to expand thereby experiencing strain. As the second layer comes up against the first, it is also compressed and comes to rest at the same above-normal pressure, and again causes strain of the corresponding section of the pen wall. As each succeeding layer of ink comes to rest, the process of ink compressing and wall straining continues up the length of the ink column. Physically, the process can be described as a pressure wave, actually a travelling pressure step, originating at the ball and moving toward the air/ink interface causing each succeeding layer of ink to come to rest.
As the last layer of ink compresses, the total kinetic energy of the ink is transformed into potential energy and is stored in the elastic deformations of stationary compressed ink and strained pen walls. This point of pressure wave action will be defined as the end of the first of four periods of wave motion.
As soon as the last layer of ink is fully compressed as the air/ink interface, the process reverses and the stored potential energy causes each successive layer to move backwards toward the air/ink interface, analogous to the action that occurs when a compressed spring is released. As the potential energy is decreased, the pressure within each ink layer and the strain within the corresponding section of the pen wall is returned to normal, i.e. zero, until the wave front reaches the ball again and the entire system has returned to normal pressure. But at the end of this period of wave action, the entire ink column is moving away from the ball with the same kinetic energy, neglecting losses, as before impact. This is the end of the second period of wave action.
During the third period, with the initial velocity of the total ink column away from the ball, the kinetic energy of each layer, starting at the ball, will be transformed into potential energy by a lowering of ink pressure to a below normal level with an attendant contraction of the corresponding pen walls.
As the process continues, the pressure wave propagates toward the air/ink interface until the system energy is stored in stationary ink, pressurized below normal, and in negatively strained pen walls. This is the end of the third period of wave action.
With the pressure in the stationary ink now below normal, the first layer of ink at the air/ink interface starts moving toward the ball. As the wave progresses, the stored potential energy is released by successive layers until the ink regains its normal pressure and initial velocity and the entire ink column is moving toward the ball as it was just before impact. This ends the fourth period.
Repeating cycles of four periods follow, but each has diminished energy because of dissipative forces within the ink/pen wall system.
The entire procedure can be viewed as a travelling pressure step originating at the ball and moving up and down the ink reservoir reflecting off of the air/ink interface reversed in sense and reflecting off of the solid ball surface unchanged in sense.
The salient feature of this analysis is centered around the end of the second period of pressure traverse. At this point, the pressure increase on the ball drops to zero, and subsequently, during the third period the pressure increase is negative (below normal pressure).
The consequence of this is that, if the ball has not moved a sufficient distance to be dislodged from its socket by the end of the second period, then it will be retained during the impact because the pressure on the ball will have been reduced below a level sufficient to continue dislodgement.
We have shown by experimentation that ball loss as a result of the effects of the travelling pressure step described above can be eliminated if the column of ink in the pen barrel above the ball is kept sufficiently short. Unfortunately, when using plastic points, many of which may have a retention force as low as 0.1 pound or less, we found that ball loss would often occur even if the column of ink above the ball did not exceed one inch in height. Because such a small quantity of ink would unduly restrict the writing life of a pen, the expedient of simply limiting the ink to fill level is not an adequate solution to the problem.